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Theorem vtocle 3277
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 9-Sep-1993.)
Hypotheses
Ref Expression
vtocle.1 𝐴 ∈ V
vtocle.2 (𝑥 = 𝐴𝜑)
Assertion
Ref Expression
vtocle 𝜑
Distinct variable groups:   𝑥,𝐴   𝜑,𝑥

Proof of Theorem vtocle
StepHypRef Expression
1 vtocle.1 . 2 𝐴 ∈ V
2 vtocle.2 . . 3 (𝑥 = 𝐴𝜑)
32vtocleg 3274 . 2 (𝐴 ∈ V → 𝜑)
41, 3ax-mp 5 1 𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1481  wcel 1988  Vcvv 3195
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-12 2045  ax-ext 2600
This theorem depends on definitions:  df-bi 197  df-an 386  df-tru 1484  df-ex 1703  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-v 3197
This theorem is referenced by:  zfrepclf  4768  tz6.12i  6201  eloprabga  6732  cfflb  9066  axcc3  9245  nn0ind-raph  11462  finxpreclem6  33204
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